No big mystery, the iTunes image is used for restoring the device, so it needs to be a complete image. The download you get on the device itself is a delta update, which only contains the changes relative to the previous version. But these changes need to be merged with the old version to create a full image of the new version, hence the need for free space.

But I gather there is absolutely no info about what this update is good for?

Back when this came out, I read a post somewhere from a guy whose wife was on her second iPhone 5. She was a constant speakerphone user, so when the speakerphone on her first iPhone stopped making sound after several months, the Apple Store gave her a new one. Shortly thereafter, it gave out again in the same way. This time, the tech went in the back room and brought back the same iPhone, but now the speakerphone was working. The guy speculated that his wife's iPhone had a custom version of iOS 6.1.3. Hence, iOS 6.1.4 pushes whatever the tech did to all our iPhones.